Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
m,n = map(int,raw_input().split())
G = [map(int,raw_input().split()) for i in xrange(m)];


row = [0 for i in xrange(m)];
col = [0 for i in xrange(n)];

for i in xrange(m):
    row[0] = min(row[0],G[i][0] - G[0][0]);

def assign(x):
    row[0] = x;
    for i in xrange(n):
        col[i] = G[0][i] - row[0];

    for i in xrange(1,m):
        row[i] = G[i][0] - col[0];

    if min(col) < 0 or min(row) < 0: return 0;
    nG = [[row[i] + col[j] for j in xrange(n)] for i in xrange(m)];
    return G == nG;

def out():
    print sum(row) + sum(col);
    for i in xrange(m):
        while row[i]:
            print "row" ,i+1;
            row[i] -= 1;

    for i in xrange(n):
        while col[i]:
            print "col", i + 1;
            col[i] -= 1;


#print row
#print col


x = -row[0];
if not assign(x): print -1;
else:
    s = x;
    e = max(G[0]);
    while s < e:
        mid = s + (e - s + 1)/2;
        if assign(mid): s = mid;
        else: e = mid -1;
    assign(x);
    a = sum(row) + sum(col);
    assign(s);
    b = sum(row) + sum(col);
    if a <= b: assign(x);
    out();